The equation of a stationary wave is $Y = 10\,\sin \,\frac{{\pi x}}{4}\,\cos \,20\,\pi t$. The distance between two consecutive nodes in metres is

If $n_1 , n_2$ and $n_3$ are the fundamental frequencies of three segments into which a string is divided, then the original fundamental frequency $n$ of the string is given by

When a wave travels in a medium, the particle displacement is given by : $y = a\,\sin \,2\pi \left( {bt - cx} \right)$ where $a, b$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if

The amplitude of a wave represented by displacement equation $y = \frac{1}{{\sqrt a }}\,\sin \,\omega t \pm \frac{1}{{\sqrt b }}\,\cos \,\omega t$ will be

A metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T (Y =$ young’s modulus, $\rho =$ density, $\alpha =$ coefficient of linear expansion) then the frequency of transverse vibration is proportional to : 

A pipe of length $85\, cm$ is closed from one end. Find the number of possible natural oscillations of air column in the pipe whose frequencies lie below $1250\, Hz$. The velocity of sound in air is $340\, m / s$